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Tempel 1
Icarus 191 (2007) 567–572 www.elsevier.com/locate/icarus
Secular light curve of Comet 9P/Tempel 1 ✩ Ignacio Ferrín Center for Fundamental Physics, University of the Andes, Mérida, Venezuela Received 29 March 2006; revised 25 July 2006
Abstract In support of the Deep Impact Mission, we have updated the secular light curve of 9P/Tempel 1 presented in Paper I [Ferrín, I., 2005. Icarus 178, 493–516], with new data sets. The secular light curves (SLC) of the comet are presented in the log and time plots (Figs. 1 and 2) and provide a clear profile of the overall shape of the envelope. We arrive at the following conclusions: (1) Improved values of 18 photometric parameters are derived including the turn on and turn off points, RON = −3.47 ± 0.05 AU, ROFF = +4.20 ± 0.05 AU, and TON = −410 ± 25 d, TOFF = +555 ± 25 d. (2) The improved SLC shows a most interesting and peculiar shape, with a linear power law of slope n = 7.7 ± 0.1 from RON = −3.47 AU to RBP = −2.08 ± 0.05 AU, and then converts to a law with curvature. The break point of the power law at RBP = −2.08 AU, mV (1, R) = 14.0 ± 0.1 mag, is interpreted as a change in sublimating something more volatile than water ice (most probably CO2 ), to water ice sublimation. In other words, the comet’s sublimation is controlled by two different substances. (3) The photometric-age (defined in Paper I) and the time-age of the comet [Ferrín, I., 2006. Icarus. In press] are recomputed, and results in a value P-AGE = 21 ± 2 and T-AGE = 11 ± 2 comet years. Thus 9P is a young comet. (4) The comet is active almost up to aphelion since the turn off point has been determined at ROFF = +4.20 ± 0.05 AU while aphelion takes place at Q = +4.74 AU. (5) The comet exhibits activity post-aphelion which is not understood. Two hypothesis are advanced to explain this behavior. © 2006 Elsevier Inc. All rights reserved. Keywords: Comets, composition; Comets, origin; Comets, dynamics
1. Introduction The Deep Impact Mission (A’Hearn et al., 2005) was a smashing success, and to place into perspective the massive amount of data collected it is convenient to have a clear picture of its past photometric behavior, in order to compare with the 2005 apparition, pre- and post-impact. The impact took place almost exactly at perihelion on July 4th, 2005. We have previously presented a secular light curve (SLC) of this comet (Ferrín, 2005, from now on Paper I), but in the short interval that transpired new data sets have been published (Hergenrother et al., 2006; Meech et al., 2004; Lisse et al., 2005; Belton et al., 2005), that need to be included and evaluated. This is evidence of the increasing pace of data acquisition on interplanetary bodies. The result is a new secular light curve that exhibits an interesting and puzzling behavior at turn on. ✩ This article originally appeared in Icarus Vol. 187/1, March 2007, pp. 326– 331. Those citing this article should use the original publication details. E-mail address: [email protected].
0019-1035/$ – see front matter © 2006 Elsevier Inc. All rights reserved. doi:10.1016/j.icarus.2006.07.032
We did attempt a reduction of the 2005 observations, but we found no agreement in the slope of the light curve exhibited by different data sets. This discrepancy may have been due to the observational method adopted, and combined with the massive amount of observations taken, did not allow the reduction work to be completed in time to be included here. 2. Current understanding A review of the working physical properties of 9P/Tempel 1 has been published by Belton et al. (2005) and their work is recommended reading on this comet. However we will specifically consider some physical properties that are relevant to our work. 2.1. Phase coefficient The phase coefficient, β, is an important parameter that is needed to reduce nuclear magnitudes and affects the calculation of the physical diameter of the nucleus. Fernandez et al. (2003), have presented a phase curve in the IAU formalism which takes
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into account the opposition effect at small phase angles, thus being a nonlinear fit to the data. Another phase curve fitted with a fifth degree polynomial was derived by Belton et al. (2005). Both works derive an absolute magnitude VN (1, 1, 0) taking into account the opposition surge at small phase angles, α. In the IAU convention, the opposition surge is taken into account. However, there are still too few determinations of the absolute magnitude in the IAU formalism, and our knowledge of the opposition effect is still meager and incomplete. Additionally the opposition effect is a brightness enhancement due to the surface texture of the cometary nucleus and it is only seen at small phase angles, typically <3◦ . On the other hand, in Paper I we have listed 9 comets from the literature, with their linear phase coefficients deduced. To be consistent, we believe it is better to continue with the linear formalism, and thus new linear phase coefficients have been deduced from the data. In the non-IAU convention, the nuclear magnitude of a comet is defined thus: V (Δ, R, α) = VN (1, 1, 0) + 5 log Δ + 2.5n log R + βα,
(1)
where VN (1, 1, 0) is the absolute magnitude, Δ is the comet– Earth distance, R is the Sun–comet distance, β is the phase coefficient, and α is the phase angle. It is easy to obtain VN (1, 1, 0) from the linear extrapolation by least squares of the phase plot, VN (1, 1, α) vs α, to α = 0◦ . With this alternative definition in mind a linear phase coefficient β = 0.069 ± 0.016 mag/deg can be derived from the data by Fernandez et al. (2003), while a value of β = 0.058 ± 0.019 mag/deg is obtained from Belton’s et al. (2005) phase plot. We see that the two phase coefficients agree quite well. In this work the mean value of variable x will be denoted by x. We find β = 0.063 ± 0.007 mag/deg and it is adopted for this comet. A list of phase coefficients for 8 other comets that were all linear fits to the data has been compiled in Table 1 of Paper I. This result is the largest phase coefficient of any comet in our data set. 2.2. Geometric albedo Fernandez et al. (2003) derived a geometric albedo pR = 0.072 ± 0.016. Lamy et al. (2005) are of the opinion that this large albedo is probably a consequence of inability to properly account for the large coma contribution in their visible observations. This reasoning might be correct, since the observations were made at R = +2.54 AU post-perihelion (log R = 0.40) while the turn off point determined in the next section is ROFF = +4.20 ± 0.05 AU (log 4.2 = 0.623). Lisse et al. (2005) are of the opinion that Fernandez et al. (2003) were observing at the mid-brightness of the rotational light curve, and conclude that if they propagate this change through their calculation, they find an albedo of pR = 0.055 ± 0.012. This value is consistent with the result from Spitzer observations by Lisse et al. (2005) who found pV = 0.041 ± 0.008 derived at R = −3.7 AU from the Sun (pre-perihelion, thus before turn on at RON = −3.47 ± 0.05 AU).
We find, however that one additional correction is needed and brings the two values into a better agreement. Hanner and Newburn (1989) and Hanner et al. (1985) have deduced the geometric albedo of the dust of several comets in the J and the K infrared bands. All of this dust is large, much larger than the wavelength of light, thus light does not know if it hit the nucleus or the dust. The large dust mimics the nucleus. This same argument has originally been made by Steigmann (1990). From 9 comets with measured geometric albedos in the J and K bands, we have found by extrapolation a conversion from R to V of pV − pR = −0.006. Thus the value by Fernandez et al. (2003) would then be in the visual pV = 0.049 ± 0.015. Combining this result with that of Lisse et al. (2005) we arrive at a mean value pV = 0.045 ± 0.009, adopted for this comet. 2.3. Color index Lowry et al. (1999) measured (B–V, V–R) = (0.46 ± 0.28, 0.37 ± 0.22). Belton and Meech (2003), obtained (B–V, V–R, R–I) = (0.744 ± 0.012, 0.475 ± 0.004, 0.473 ± 0.005), while Meech et al. (2004) derived V–R = 0.47 ± 0.01. In their review paper on 9P/Tempel 1, Belton et al. (2005) adopt a value for V–R = 0.56 ± 0.02 which is a personal communication from Hsieh and Meech. We have adopted as mean values (B–V, V–R, R–I) = (0.60 ± 0.14, 0.47 ± 0.08, 0.47 ± 0.01) for this comet. 3. Updated secular light curve 3.1. Absolute nuclear magnitude There have been many nuclear observations some allowing the determination of the absolute nuclear magnitude VN (1, 1, 0). They have been compiled and averaged in Table 1. Near nuclear observations have been reported by Chen and Jewitt (1994), Scotti (1995), Weissman et al. (1999), Lowry et al. (1999), Meech et al. (2000), Lamy et al. (2001), Lowry and Fitzsimmons (2001), Meech (2002), Fernandez et al. (2003), Belton et al. (2005), Lisse et al. (2005), and Hergenrother et al. (2006). One of the useful byproducts of the SLCs is that it allows the determination of nucleus contamination by the coma (cc), indicated by an observational distance less that RON or ROFF , or a nuclear magnitude too bright. Lisse et al. (2005) give little information on their unpublished measurements. Scotti’s value looks too bright in comparison with the others, and was taken with no filter. These values (indicated by cc) were dropped in Table 1 before calculating the average. Most photometric observation were re-reduced using the adopted new phase coefficient β and new V–R value, giving an absolute magnitude more in accord with the other values listed in Table 1. The absolute nuclear magnitude of the different groups now converge to a very similar value of VN (1, 1, 0) = 15.29 ± 0.04. With this upgraded value the reported discrepancies in the nuclear magnitudes of 9P/Tempel 1 (Paper I) disappear. The mean nuclear line has been depicted in the log plot (Fig. 1), takes the form of a pyramid of slope 5.0 at the bottom of the
Secular light curve of Comet 9P/Tempel 1
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Table 1 Absolute nuclear magnitudes of 9P/Tempel 1, VN (1, 1, 0) cc = coma contamination if R < RON = −3.47 AU or R < ROFF = +4.20 AU # 1 2 3 4 5 6 7 8 9 10
Date
Δt [d]
Δ [AU]
R [AU]
VN (1, 1, 0)
Reference
1995 1997/12/31 1998/12/09 1998/12/xx 1999/02/xx 1999/03/18 1998–2002 2001/09/23 1997/12/29 2004/02/26 1997–2002 Mean
– −732 −388 −382 −321 −285 – +631 −369 +236 –
– 3.53 2.71 2.63 2.14 2.28 – 3.55 3.84 3.04 –
– cc? −4.48 −3.36 −3.35 cc −3.04 −2.87 cc – +4.25 −4.21 3.92 cc? –
15.1 ± 0.7 15.25 ± 0.20 15.33 ± 0.10 15.32 ± 0.04
Scotti (1995) Lamy et al. (2001) Lowry and Fitzsimmons (2001) Weissman et al. (1999)
14.63 ± 0.30 15.27 ± 0.20 15.34 ± 0.09 15.28 ± 0.10 15.15 15.27 ± 0.09 15.29 ± 0.04
Meech et al. (2000) Fernandez et al. (2003) Hergenrother et al. (2006) Meech et al. (2004) Lisse et al. (2005) Belton et al. (2005) This work
Fig. 1. Updated secular light curve of Comet 9P/Tempel 1, log plot. The most significant feature of this SLC is the break point (BP) in the power law before perihelion, at RBP = −2.08 ± 0.05 AU. We interpret this BP as the switch from CO2 sublimation to H2 O sublimation. x indicates mean values. Table 1 is a compilation of absolute nuclear magnitudes with the mean value calculated in the text. Notice also the activity post-aphelion. LF = Lowry and Fitzsimmons (2001). CJ = Chen and Jewitt (1994). HMCSM = Hergenrother et al. (2006). LTAWW = Lamy et al. (2001). FMLAPB = Fernandez et al. (2003). M et al. = Meech et al. (2004). B et al. = Belton et al. (2005).
plot, and corresponds to the mean V value of the rotational light curve, whose peak to valley amplitude is AROT = 0.7 magnitudes (Belton et al., 2005).
VMIN = C + 2.5 log bc,
3.2. Effective diameter of the comet
1/4 DEFFE = 2 abc2 ,
It is common to see the effective diameter of the nucleus defined in the literature as D = (abc)1/3 . However, the mean nuclear magnitude of a nucleus of semi-axis a, b, c, is defined in terms of the mean V value of the rotational light curve, and this value corresponds to: VMAX = C + 2.5 log ac,
1/2 VN (1, 1, 0) = (VMAX + VMIN )/2 = C + 2.5 log abc2 , (2) (3)
where C is the zero point constant and a b c. Notice the weight of semi-axis c which is usually poorly determined and thus assumed equal to b. Now we want to relate this diameter to the absolute nuclear magnitude. The diameter of the nucleus is customarily derived from the formula (Jewitt, 1991)
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pV rN2 = 2.25 × 1022 R 2 Δ2 100.4(m −m+βα) ,
I. Ferrín / Icarus 191 (2007) 567–572
(4)
where pV is the geometric albedo, rN is the nuclear radius, m is the solar magnitude (mV = −26.74, mV = −27.10), m is the observed magnitude, R is the Sun–comet distance, Δ is the Earth–comet distance, α is the phase angle, and β the phase coefficient. In this equation rN is given in meters, and R and Δ are in AU. This equation can be simplified considerably if (a) we use the absolute nuclear magnitude VN (1, 1, 0), (b) if we replace the radius by the effective diameter, DEFFE , and (c) if we calculate this value in km not in m. The result is a much more compact and amicable formula: 2 /4 = 5.654 − 0.4VN (1, 1, 0), log pV DEFFE (5) if the absolute nuclear magnitude in the visual, VN (1, 1, 0), is used. If instead, the absolute nuclear magnitude in the red is used, RN (1, 1, 0), then: 2 /4 = 5.510 − 0.4RN (1, 1, 0). log pR DEFFE (6) Notice that now in these two formulas DEFFE (in km), VN (1, 1, 0), and RN (1, 1, 0) all correspond to the mean value of the rotational light curve. Using the mean albedo adopted above, the mean absolute nuclear magnitude from Table 1, and Eq. (5), we find a mean effective diameter DEFFE = 5.54 ± 0.5 km from ground based observations. The Deep Impact Spacecraft (DI) measured a long axis a = 3.8 km and a short axis b = 2.45 km (A’Hearn et al., 2005) for this comet. To be consistent we have to use Eq. (3) to determine the diameter. With this formula the effective diameter is DEFFE = 5.47 ± 0.2 km. The agreement between the two independent methodologies could not be better, and it is the result of our careful calculation of phase coefficient, geometric albedo and absolute nuclear magnitude. This diameter is probably one of the best known of all comets, due to the small ground based observational error.
substances, of their abundance, and of the depth of the sublimating layers, thus the above estimate is only an approximated value. A precise value will have to wait until a theoretical model is developed including the above parameters. 3.4. Turn on and turn off points They can be determined with great accuracy from Figs. 1 and 2. We measure RON = −3.47 ± 0.05 AU. Hergenrother et al. (2006) observed the comet almost at aphelion (R = +4.24 AU) and after making a 13750 s exposure found the comet devoid of coma. Thus the turn off point must have taken place recently at ROFF = +4.20 ± 0.05 AU. According to this observation the nucleus should be off at aphelion. From Fig. 2 we find TON = −410 ± 25 d, TOFF = +555 ± 25 d. We did not try to reconcile the values found from the log and the time plots. With this information we calculate that the active time is TACTIVITY = 965 ± 35 d or ∼2.6 years. 3.5. Photometric-age and time-age In Paper I we defined photometric age, P-AGE, as a parameter that measures the activity of the comet P-AGE = 1440/[ASEC (RON + ROFF )], where ASEC is the amplitude of the secular light curve measured from the log plot as ASEC = VN (1, 1, 0) − mV (1, 1). With this formula we find P-AGE = 21 ± 2 cy, where cy stands for comet years to clarify that this are relative numbers not yet calibrated in Earth’s years. We conclude that the comet is a young object. Ferrín (2006) defined a new cometary age called timeage or T-AGE using a definition similar to P-AGE, T-AGE = 90240/[ASEC (TON + TOFF )] except that now the information comes from the time plot. For 9P/Tempel 1 we find from Fig. 2 T-AGE = 11 ± 2 cy. Once again we find that this is a young comet.
3.3. Power law break point The SLC exhibits a power law break at RBP = −2.08 ± 0.05 AU from the Sun. Before this point the power law is linear in the log plot with slope R +7.7 . After that point there is curvature in the SLC. Curvature is an indication of water ice sublimation, because the vapor pressure vs temperature of water ice shows strong curvature. A linear law is indication of CO2 or CO. H2 O and CO2 have been detected in 9P (A’Hearn et al., 2005). Delsemme (1982) has plotted the sublimation of several substances vs R. His Fig. 1 for water ice shows a point r0 = 2.5 AU, where 2.5% of the energy goes into sublimation, and 97.5% is reradiated to space. Thus this could be considered as the initiation of water ice sublimation. Fig. 1 for 9P shows the initiation very near to this point at RON = −2.08 AU. However, Delsemme’s calculation has been questioned by Meech and Svoren (2005), who find that selecting modern values for the parameters water initiation takes place further out in the orbit. The power law break point is a function of the sublimating
3.6. Activity post-aphelion In Paper I it was suggested that the comet exhibited activity post-aphelion, and in this work that suspicion is confirmed. In particular, a snapshot observation by Lowry et al. (1999) taken in 1995, August 27 (at R = −3.511 AU) revealed the comet with a faint coma. This is a well calibrated CCD observation. Surprisingly another observation by Lowry and Fitzsimmons (2001) made in 1998, December 10 (at R = −3.36 AU) revealed a stellar nucleus. Observations published by Belton et al. (2005) reveal activity post aphelion clearly. For comparison the turn on point is at RON = −3.47 AU. Thus there is some evidence to conclude that the comet is active post aphelion, but the extent and intensity of this activity has not been sampled completely. There is no contradiction with the observations by Lowry and Fitzsimmons (2001) because the comet may have exhibited a nondetectable coma at the time of their observations.
Secular light curve of Comet 9P/Tempel 1
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Fig. 2. Updated secular light curve of Comet 9P/Tempel 1, time plot. Notice the very smooth decay in brightness after perihelion. The square with a dot inside is a snapshot observation by Lowry et al. (1999). The comet reaches maximum brightness 10 ± 4 days before perihelion.
3.7. Significance of the break point
4. Future observational conditions
It has been known for some time that comets do sublimate different species at the same time (see, for example, Biver et al. (1997) for Comet 1995 O1 Hale–Bopp). However, there is always a major species that controls sublimation. A change of controlling substance may have been seen in the secular light curves of Comets 1P, 81P and 21P (Paper I). Our work leaves no doubt that two substances can control sublimation on the same comet at different orbital times. The question is how. The break point at R = −2.08 AU can be interpreted with two hypothesis, although others may be viable. In the first hypothesis there is an underground layer of CO2 that gets heated post-aphelion, and that controls sublimation up to RBP , when H2 O overwhelms the production rate changing the slope. This hypothesis would require that the CO2 layer be near the surface. In the second hypothesis, post-perihelion the thermal wave penetrates the nucleus, sublimates a deep layer of CO2 up to aphelion, and remnants of these molecules are recondensed in the upper layers of the nucleus as it cools off. When the comet approaches the Sun post-aphelion, these remaining molecules are sublimated and produce the observed activity. It is beyond the scope of this paper to create a model to discriminate between these two hypothesis. What remains certain is that the double sublimation exhibited by 9P, 1P, 81P and 21P have profound implications for the interior models and structure of these cometary nuclei, and for our understanding of how a cometary nucleus sublimates into space.
The comet has an orbital period of 5.51 yr, thus apparitions repeat almost exactly every 11.02 years. Notice how the 1972, 1983, 1994, 2005 have perihelions in July 15th, 10th, 3rd, 5th, while in 1978, 1989, 2000 the perihelions were in January 11th, 4th, and 2nd. A complete SLC every 11 years would allow the determination of secular effects and the confirmation of postaphelion activity. In that regard, the comet reaches aphelion in 20080407 (YYYYMMDD) at elongation E = 42◦ and decreasing, thus approaching conjunction with the Sun. E = 90◦ and increasing in 20080926 when observation may commence, and reaches opposition in 20081218 at E = 176◦ . It again becomes increasingly difficult to observe in 20090309 at E = 90◦ and decreasing, but in 20091103 E = 90◦ and increasing. Finally, the comet reaches the turn on point, RON , in 20091124 at E = 108◦ and increasing. In conclusion the interval aphelion-RON will be only partially observable in 2008–2009. 5. Conclusions The main results of this work are: (a) 9P/Tempel 1 is a young object as measured by two definitions of age, P-AGE = 21 ± 2 cy and T-AGE = 11 ± 2 cy. This is in agreement with the smooth surface structure imaged by Deep Impact.
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(b) The comet exhibits double sublimation at turn on, showing a linear portion that changes to curvature at a break point RBP = −2.08 ± 0.05 AU pre-perihelion. This critical point has profound implications for our understanding of how a cometary nucleus sublimates into space. (c) Over 18 physical parameters of the comet have been updated and appear in Figs. 1 and 2. (d) A very precise mean absolute nuclear magnitude has been determined as VN (1, 1, 0) = 15.29 ± 0.04 (Table 1). (e) When this value is combined with a mean geometric albedo in the visual pV = 0.045 ± 0.009, an effective diameter DEFFE = 5.54 ± 0.5 km is derived from ground based observations in excellent agreement with the value derived from the Deep Impact Spacecraft (D = 5.47 ± 0.2 km). The information on this and other comets is regularly updated at the site: http://webdelprofesor.ula.ve/ciencias/ferrin. Acknowledgments To Oliver Hainaut and Carl Hergenrother for their suggestions to improve the scientific quality of this paper. To the Council for Scientific and Technological Development of the University of the Andes, for support through grant number C1281-04-05-B. References A’Hearn, M.F., and 32 colleagues, 2005. Deep Impact: Excavating Comet Tempel 1. Science 310, 258–264. Belton, M.J.S., Meech, K.J., 2003. Homing in on the period of 9P/Tempel. In: AAS DPS Meeting 35. Abstract 38.04. Belton, M.J.S., and 15 colleagues, 2005. Deep Impact: Working properties for the target nucleus—Comet 9P/Tempel 1. Space Sci. Rev. 117, 137–160. Biver, N., and 22 colleagues, 1997. Long-term evolution of the outgassing of Comet Hale–Bopp from radio observations. Earth Moon Planets 78, 5–11. Chen, J., Jewitt, D., 1994. On the rate at which comets split. Icarus 108, 265– 271. Delsemme, A.H., 1982. Chemical composition of the cometary nucleus. In: Wilkening, L. (Ed.), Comets. Univ. of Arizona Press, Tucson, AZ, pp. 85– 130. Fernandez, Y.R., Meech, K.J., Lisse, C.M., A’Hearn, M.F., Pittichová, J., Belton, M.J.S., 2003. The nucleus of Deep Impact target Comet 9P/Tempel 1. Icarus 164, 481–491. Ferrín, I., 2005. Secular light curve of Comet 28P/Neujmin 1, and of comets targets of Spacecraft, 1P/Halley, 9P/Tempel 1, 19P/Borrelly, 21P/Grigg–
Skejellerup, 26P/Giacobinni–Zinner, 67P/Chruyumov–Gersimenko, 81P/ Wild 2. Icarus 178, 493–516. Ferrín, I., 2006. Secular light curve of comets. II. 133P/Elst–Pizarro. Icarus. In press. Hanner, M.S., Tedesco, E., Tokunaga, A.T., Veeder, G.J., Lester, D.F., Witteborn, F.C., Bregamn, J.D., Gradies, J., Lebofsky, L., 1985. The dust coma of periodic Comet Churyumov–Gerasimenko. Icarus 64, 11–19. Hanner, M.S., Newburn, R.L., 1989. Infrared photometry of Comet Wilson (1986l) at two epochs. Astron. J. 97, 254–261. Hergenrother, C.W., Mueller, B.E.A., Campins, H., Samarasinha, H.H., McCarthy Jr., D.W., 2006. R and J-band photometry of Comets 2P/Encke and 9P/Tempel 1. Icarus 181, 156–161. Jewitt, D.C., 1991. Cometary photometry. In: Newburn, R.L., Neugebauer, M., Rahe, J. (Eds.), Comets in the Post-Halley Era, vol. 1. Kluwer, Dordrecht, Boston, London, pp. 19–65. Lamy, P.L., Toth, I., A’Hearn, M.F., Weaver, H.A., Weissman, P.R., 2001. Hubble Space Telescope observations of the nucleus of Comet 9P/Tempel 1. Icarus 154, 337–344. Lamy, P.L., Toth, I., Fernandez, Y.R., Weaver, H.A., 2005. The sizes, shapes, albedos, and colors of cometary nuclei. In: Festou, M., Keller, H.U., Weaver, H.A. (Eds.), Comets II. Univ. of Arizona Press, Tucson, AZ, pp. 223–264. Lisse, C.M., A’Hearn, M.F., Groussin, O., Fernandez, Y.R., Belton, M.J.S., Van Cleve, J.E., Charmandaris, V., Meech, K.J., McGleam, C., 2005. Rotationally resolved 8–35 micron Spitzer Space Telescope observations of the nucleus of Comet 9P/Tempel 1. Astrophys. J. 625, L139–L142. Lowry, S.C., Fitzsimmons, A., Cartwright, L.M., Williams, I.P., 1999. CCD photometry of distant comets. Astron. Astrophys. 349, 649–659. Lowry, S.C., Fitzsimmons, A., 2001. CCD photometry of distant comets. II. Astron. Astrophys. 365, 204–213. Meech, K.J., 2002. The Deep Impact Mission and the AAVSO. JAAVSO 31, 27–33. Meech, K.J., Svoren, J., 2005. Using cometary activity to trace the physical and chemical evolution of cometary nuclei. In: Festou, M., Keller, H.U., Weaver, H.E. (Eds.), Comets II. Univ. of Arizona Press, Tucson, AZ, pp. 317–335. Meech, K.J., A’Hearn, M.F., McFadden, L., Belton, M.J.S., Delamere, A., Kissel, J., Klassen, K., Yeomans, D., Melosh, J., Schultz, P., Sunshine, J., Veverka, J., 2000. Deep Impact—Exploring the interior of a comet. In: Lemarchand, G., Meech, K.J. (Eds.), A New Era in Bioastronomy. In: ASP Conference Series, vol. 213, pp. 235–242. Meech, K.J., Hainaut, O.R., Marsden, B.G., 2004. Comet nucleus size distribution from HST and Keck telescopes. Icarus 170, 463–491. Scotti, J., 1995. Comet nuclear magnitudes. In: DPS Meeting, Session 43. Bull. Am. Astron. Soc. 26, 185. Steigmann, G.A., 1990. Surface conditions on the nucleus of Comet 1P/Halley. J. Brit. Astron. Assoc. 100, L6. Weissman, P., Doressoundiram, Hicks, M., Chamberlin, A., Sykes, M., Larson, S., Hergenrother, C., 1999. CCD photometry of comet and asteroid targets of spacecraft missions. In: AAS DPS Meeting 31. Abstract 30.03.
Secular light curve of Comet 9P/Tempel 1 ✩ Ignacio Ferrín Center for Fundamental Physics, University of the Andes, Mérida, Venezuela Received 29 March 2006; revised 25 July 2006
Abstract In support of the Deep Impact Mission, we have updated the secular light curve of 9P/Tempel 1 presented in Paper I [Ferrín, I., 2005. Icarus 178, 493–516], with new data sets. The secular light curves (SLC) of the comet are presented in the log and time plots (Figs. 1 and 2) and provide a clear profile of the overall shape of the envelope. We arrive at the following conclusions: (1) Improved values of 18 photometric parameters are derived including the turn on and turn off points, RON = −3.47 ± 0.05 AU, ROFF = +4.20 ± 0.05 AU, and TON = −410 ± 25 d, TOFF = +555 ± 25 d. (2) The improved SLC shows a most interesting and peculiar shape, with a linear power law of slope n = 7.7 ± 0.1 from RON = −3.47 AU to RBP = −2.08 ± 0.05 AU, and then converts to a law with curvature. The break point of the power law at RBP = −2.08 AU, mV (1, R) = 14.0 ± 0.1 mag, is interpreted as a change in sublimating something more volatile than water ice (most probably CO2 ), to water ice sublimation. In other words, the comet’s sublimation is controlled by two different substances. (3) The photometric-age (defined in Paper I) and the time-age of the comet [Ferrín, I., 2006. Icarus. In press] are recomputed, and results in a value P-AGE = 21 ± 2 and T-AGE = 11 ± 2 comet years. Thus 9P is a young comet. (4) The comet is active almost up to aphelion since the turn off point has been determined at ROFF = +4.20 ± 0.05 AU while aphelion takes place at Q = +4.74 AU. (5) The comet exhibits activity post-aphelion which is not understood. Two hypothesis are advanced to explain this behavior. © 2006 Elsevier Inc. All rights reserved. Keywords: Comets, composition; Comets, origin; Comets, dynamics
1. Introduction The Deep Impact Mission (A’Hearn et al., 2005) was a smashing success, and to place into perspective the massive amount of data collected it is convenient to have a clear picture of its past photometric behavior, in order to compare with the 2005 apparition, pre- and post-impact. The impact took place almost exactly at perihelion on July 4th, 2005. We have previously presented a secular light curve (SLC) of this comet (Ferrín, 2005, from now on Paper I), but in the short interval that transpired new data sets have been published (Hergenrother et al., 2006; Meech et al., 2004; Lisse et al., 2005; Belton et al., 2005), that need to be included and evaluated. This is evidence of the increasing pace of data acquisition on interplanetary bodies. The result is a new secular light curve that exhibits an interesting and puzzling behavior at turn on. ✩ This article originally appeared in Icarus Vol. 187/1, March 2007, pp. 326– 331. Those citing this article should use the original publication details. E-mail address: [email protected].
0019-1035/$ – see front matter © 2006 Elsevier Inc. All rights reserved. doi:10.1016/j.icarus.2006.07.032
We did attempt a reduction of the 2005 observations, but we found no agreement in the slope of the light curve exhibited by different data sets. This discrepancy may have been due to the observational method adopted, and combined with the massive amount of observations taken, did not allow the reduction work to be completed in time to be included here. 2. Current understanding A review of the working physical properties of 9P/Tempel 1 has been published by Belton et al. (2005) and their work is recommended reading on this comet. However we will specifically consider some physical properties that are relevant to our work. 2.1. Phase coefficient The phase coefficient, β, is an important parameter that is needed to reduce nuclear magnitudes and affects the calculation of the physical diameter of the nucleus. Fernandez et al. (2003), have presented a phase curve in the IAU formalism which takes
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into account the opposition effect at small phase angles, thus being a nonlinear fit to the data. Another phase curve fitted with a fifth degree polynomial was derived by Belton et al. (2005). Both works derive an absolute magnitude VN (1, 1, 0) taking into account the opposition surge at small phase angles, α. In the IAU convention, the opposition surge is taken into account. However, there are still too few determinations of the absolute magnitude in the IAU formalism, and our knowledge of the opposition effect is still meager and incomplete. Additionally the opposition effect is a brightness enhancement due to the surface texture of the cometary nucleus and it is only seen at small phase angles, typically <3◦ . On the other hand, in Paper I we have listed 9 comets from the literature, with their linear phase coefficients deduced. To be consistent, we believe it is better to continue with the linear formalism, and thus new linear phase coefficients have been deduced from the data. In the non-IAU convention, the nuclear magnitude of a comet is defined thus: V (Δ, R, α) = VN (1, 1, 0) + 5 log Δ + 2.5n log R + βα,
(1)
where VN (1, 1, 0) is the absolute magnitude, Δ is the comet– Earth distance, R is the Sun–comet distance, β is the phase coefficient, and α is the phase angle. It is easy to obtain VN (1, 1, 0) from the linear extrapolation by least squares of the phase plot, VN (1, 1, α) vs α, to α = 0◦ . With this alternative definition in mind a linear phase coefficient β = 0.069 ± 0.016 mag/deg can be derived from the data by Fernandez et al. (2003), while a value of β = 0.058 ± 0.019 mag/deg is obtained from Belton’s et al. (2005) phase plot. We see that the two phase coefficients agree quite well. In this work the mean value of variable x will be denoted by x. We find β = 0.063 ± 0.007 mag/deg and it is adopted for this comet. A list of phase coefficients for 8 other comets that were all linear fits to the data has been compiled in Table 1 of Paper I. This result is the largest phase coefficient of any comet in our data set. 2.2. Geometric albedo Fernandez et al. (2003) derived a geometric albedo pR = 0.072 ± 0.016. Lamy et al. (2005) are of the opinion that this large albedo is probably a consequence of inability to properly account for the large coma contribution in their visible observations. This reasoning might be correct, since the observations were made at R = +2.54 AU post-perihelion (log R = 0.40) while the turn off point determined in the next section is ROFF = +4.20 ± 0.05 AU (log 4.2 = 0.623). Lisse et al. (2005) are of the opinion that Fernandez et al. (2003) were observing at the mid-brightness of the rotational light curve, and conclude that if they propagate this change through their calculation, they find an albedo of pR = 0.055 ± 0.012. This value is consistent with the result from Spitzer observations by Lisse et al. (2005) who found pV = 0.041 ± 0.008 derived at R = −3.7 AU from the Sun (pre-perihelion, thus before turn on at RON = −3.47 ± 0.05 AU).
We find, however that one additional correction is needed and brings the two values into a better agreement. Hanner and Newburn (1989) and Hanner et al. (1985) have deduced the geometric albedo of the dust of several comets in the J and the K infrared bands. All of this dust is large, much larger than the wavelength of light, thus light does not know if it hit the nucleus or the dust. The large dust mimics the nucleus. This same argument has originally been made by Steigmann (1990). From 9 comets with measured geometric albedos in the J and K bands, we have found by extrapolation a conversion from R to V of pV − pR = −0.006. Thus the value by Fernandez et al. (2003) would then be in the visual pV = 0.049 ± 0.015. Combining this result with that of Lisse et al. (2005) we arrive at a mean value pV = 0.045 ± 0.009, adopted for this comet. 2.3. Color index Lowry et al. (1999) measured (B–V, V–R) = (0.46 ± 0.28, 0.37 ± 0.22). Belton and Meech (2003), obtained (B–V, V–R, R–I) = (0.744 ± 0.012, 0.475 ± 0.004, 0.473 ± 0.005), while Meech et al. (2004) derived V–R = 0.47 ± 0.01. In their review paper on 9P/Tempel 1, Belton et al. (2005) adopt a value for V–R = 0.56 ± 0.02 which is a personal communication from Hsieh and Meech. We have adopted as mean values (B–V, V–R, R–I) = (0.60 ± 0.14, 0.47 ± 0.08, 0.47 ± 0.01) for this comet. 3. Updated secular light curve 3.1. Absolute nuclear magnitude There have been many nuclear observations some allowing the determination of the absolute nuclear magnitude VN (1, 1, 0). They have been compiled and averaged in Table 1. Near nuclear observations have been reported by Chen and Jewitt (1994), Scotti (1995), Weissman et al. (1999), Lowry et al. (1999), Meech et al. (2000), Lamy et al. (2001), Lowry and Fitzsimmons (2001), Meech (2002), Fernandez et al. (2003), Belton et al. (2005), Lisse et al. (2005), and Hergenrother et al. (2006). One of the useful byproducts of the SLCs is that it allows the determination of nucleus contamination by the coma (cc), indicated by an observational distance less that RON or ROFF , or a nuclear magnitude too bright. Lisse et al. (2005) give little information on their unpublished measurements. Scotti’s value looks too bright in comparison with the others, and was taken with no filter. These values (indicated by cc) were dropped in Table 1 before calculating the average. Most photometric observation were re-reduced using the adopted new phase coefficient β and new V–R value, giving an absolute magnitude more in accord with the other values listed in Table 1. The absolute nuclear magnitude of the different groups now converge to a very similar value of VN (1, 1, 0) = 15.29 ± 0.04. With this upgraded value the reported discrepancies in the nuclear magnitudes of 9P/Tempel 1 (Paper I) disappear. The mean nuclear line has been depicted in the log plot (Fig. 1), takes the form of a pyramid of slope 5.0 at the bottom of the
Secular light curve of Comet 9P/Tempel 1
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Table 1 Absolute nuclear magnitudes of 9P/Tempel 1, VN (1, 1, 0) cc = coma contamination if R < RON = −3.47 AU or R < ROFF = +4.20 AU # 1 2 3 4 5 6 7 8 9 10
Date
Δt [d]
Δ [AU]
R [AU]
VN (1, 1, 0)
Reference
1995 1997/12/31 1998/12/09 1998/12/xx 1999/02/xx 1999/03/18 1998–2002 2001/09/23 1997/12/29 2004/02/26 1997–2002 Mean
– −732 −388 −382 −321 −285 – +631 −369 +236 –
– 3.53 2.71 2.63 2.14 2.28 – 3.55 3.84 3.04 –
– cc? −4.48 −3.36 −3.35 cc −3.04 −2.87 cc – +4.25 −4.21 3.92 cc? –
15.1 ± 0.7 15.25 ± 0.20 15.33 ± 0.10 15.32 ± 0.04
Scotti (1995) Lamy et al. (2001) Lowry and Fitzsimmons (2001) Weissman et al. (1999)
14.63 ± 0.30 15.27 ± 0.20 15.34 ± 0.09 15.28 ± 0.10 15.15 15.27 ± 0.09 15.29 ± 0.04
Meech et al. (2000) Fernandez et al. (2003) Hergenrother et al. (2006) Meech et al. (2004) Lisse et al. (2005) Belton et al. (2005) This work
Fig. 1. Updated secular light curve of Comet 9P/Tempel 1, log plot. The most significant feature of this SLC is the break point (BP) in the power law before perihelion, at RBP = −2.08 ± 0.05 AU. We interpret this BP as the switch from CO2 sublimation to H2 O sublimation. x indicates mean values. Table 1 is a compilation of absolute nuclear magnitudes with the mean value calculated in the text. Notice also the activity post-aphelion. LF = Lowry and Fitzsimmons (2001). CJ = Chen and Jewitt (1994). HMCSM = Hergenrother et al. (2006). LTAWW = Lamy et al. (2001). FMLAPB = Fernandez et al. (2003). M et al. = Meech et al. (2004). B et al. = Belton et al. (2005).
plot, and corresponds to the mean V value of the rotational light curve, whose peak to valley amplitude is AROT = 0.7 magnitudes (Belton et al., 2005).
VMIN = C + 2.5 log bc,
3.2. Effective diameter of the comet
1/4 DEFFE = 2 abc2 ,
It is common to see the effective diameter of the nucleus defined in the literature as D = (abc)1/3 . However, the mean nuclear magnitude of a nucleus of semi-axis a, b, c, is defined in terms of the mean V value of the rotational light curve, and this value corresponds to: VMAX = C + 2.5 log ac,
1/2 VN (1, 1, 0) = (VMAX + VMIN )/2 = C + 2.5 log abc2 , (2) (3)
where C is the zero point constant and a b c. Notice the weight of semi-axis c which is usually poorly determined and thus assumed equal to b. Now we want to relate this diameter to the absolute nuclear magnitude. The diameter of the nucleus is customarily derived from the formula (Jewitt, 1991)
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pV rN2 = 2.25 × 1022 R 2 Δ2 100.4(m −m+βα) ,
I. Ferrín / Icarus 191 (2007) 567–572
(4)
where pV is the geometric albedo, rN is the nuclear radius, m is the solar magnitude (mV = −26.74, mV = −27.10), m is the observed magnitude, R is the Sun–comet distance, Δ is the Earth–comet distance, α is the phase angle, and β the phase coefficient. In this equation rN is given in meters, and R and Δ are in AU. This equation can be simplified considerably if (a) we use the absolute nuclear magnitude VN (1, 1, 0), (b) if we replace the radius by the effective diameter, DEFFE , and (c) if we calculate this value in km not in m. The result is a much more compact and amicable formula: 2 /4 = 5.654 − 0.4VN (1, 1, 0), log pV DEFFE (5) if the absolute nuclear magnitude in the visual, VN (1, 1, 0), is used. If instead, the absolute nuclear magnitude in the red is used, RN (1, 1, 0), then: 2 /4 = 5.510 − 0.4RN (1, 1, 0). log pR DEFFE (6) Notice that now in these two formulas DEFFE (in km), VN (1, 1, 0), and RN (1, 1, 0) all correspond to the mean value of the rotational light curve. Using the mean albedo adopted above, the mean absolute nuclear magnitude from Table 1, and Eq. (5), we find a mean effective diameter DEFFE = 5.54 ± 0.5 km from ground based observations. The Deep Impact Spacecraft (DI) measured a long axis a = 3.8 km and a short axis b = 2.45 km (A’Hearn et al., 2005) for this comet. To be consistent we have to use Eq. (3) to determine the diameter. With this formula the effective diameter is DEFFE = 5.47 ± 0.2 km. The agreement between the two independent methodologies could not be better, and it is the result of our careful calculation of phase coefficient, geometric albedo and absolute nuclear magnitude. This diameter is probably one of the best known of all comets, due to the small ground based observational error.
substances, of their abundance, and of the depth of the sublimating layers, thus the above estimate is only an approximated value. A precise value will have to wait until a theoretical model is developed including the above parameters. 3.4. Turn on and turn off points They can be determined with great accuracy from Figs. 1 and 2. We measure RON = −3.47 ± 0.05 AU. Hergenrother et al. (2006) observed the comet almost at aphelion (R = +4.24 AU) and after making a 13750 s exposure found the comet devoid of coma. Thus the turn off point must have taken place recently at ROFF = +4.20 ± 0.05 AU. According to this observation the nucleus should be off at aphelion. From Fig. 2 we find TON = −410 ± 25 d, TOFF = +555 ± 25 d. We did not try to reconcile the values found from the log and the time plots. With this information we calculate that the active time is TACTIVITY = 965 ± 35 d or ∼2.6 years. 3.5. Photometric-age and time-age In Paper I we defined photometric age, P-AGE, as a parameter that measures the activity of the comet P-AGE = 1440/[ASEC (RON + ROFF )], where ASEC is the amplitude of the secular light curve measured from the log plot as ASEC = VN (1, 1, 0) − mV (1, 1). With this formula we find P-AGE = 21 ± 2 cy, where cy stands for comet years to clarify that this are relative numbers not yet calibrated in Earth’s years. We conclude that the comet is a young object. Ferrín (2006) defined a new cometary age called timeage or T-AGE using a definition similar to P-AGE, T-AGE = 90240/[ASEC (TON + TOFF )] except that now the information comes from the time plot. For 9P/Tempel 1 we find from Fig. 2 T-AGE = 11 ± 2 cy. Once again we find that this is a young comet.
3.3. Power law break point The SLC exhibits a power law break at RBP = −2.08 ± 0.05 AU from the Sun. Before this point the power law is linear in the log plot with slope R +7.7 . After that point there is curvature in the SLC. Curvature is an indication of water ice sublimation, because the vapor pressure vs temperature of water ice shows strong curvature. A linear law is indication of CO2 or CO. H2 O and CO2 have been detected in 9P (A’Hearn et al., 2005). Delsemme (1982) has plotted the sublimation of several substances vs R. His Fig. 1 for water ice shows a point r0 = 2.5 AU, where 2.5% of the energy goes into sublimation, and 97.5% is reradiated to space. Thus this could be considered as the initiation of water ice sublimation. Fig. 1 for 9P shows the initiation very near to this point at RON = −2.08 AU. However, Delsemme’s calculation has been questioned by Meech and Svoren (2005), who find that selecting modern values for the parameters water initiation takes place further out in the orbit. The power law break point is a function of the sublimating
3.6. Activity post-aphelion In Paper I it was suggested that the comet exhibited activity post-aphelion, and in this work that suspicion is confirmed. In particular, a snapshot observation by Lowry et al. (1999) taken in 1995, August 27 (at R = −3.511 AU) revealed the comet with a faint coma. This is a well calibrated CCD observation. Surprisingly another observation by Lowry and Fitzsimmons (2001) made in 1998, December 10 (at R = −3.36 AU) revealed a stellar nucleus. Observations published by Belton et al. (2005) reveal activity post aphelion clearly. For comparison the turn on point is at RON = −3.47 AU. Thus there is some evidence to conclude that the comet is active post aphelion, but the extent and intensity of this activity has not been sampled completely. There is no contradiction with the observations by Lowry and Fitzsimmons (2001) because the comet may have exhibited a nondetectable coma at the time of their observations.
Secular light curve of Comet 9P/Tempel 1
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Fig. 2. Updated secular light curve of Comet 9P/Tempel 1, time plot. Notice the very smooth decay in brightness after perihelion. The square with a dot inside is a snapshot observation by Lowry et al. (1999). The comet reaches maximum brightness 10 ± 4 days before perihelion.
3.7. Significance of the break point
4. Future observational conditions
It has been known for some time that comets do sublimate different species at the same time (see, for example, Biver et al. (1997) for Comet 1995 O1 Hale–Bopp). However, there is always a major species that controls sublimation. A change of controlling substance may have been seen in the secular light curves of Comets 1P, 81P and 21P (Paper I). Our work leaves no doubt that two substances can control sublimation on the same comet at different orbital times. The question is how. The break point at R = −2.08 AU can be interpreted with two hypothesis, although others may be viable. In the first hypothesis there is an underground layer of CO2 that gets heated post-aphelion, and that controls sublimation up to RBP , when H2 O overwhelms the production rate changing the slope. This hypothesis would require that the CO2 layer be near the surface. In the second hypothesis, post-perihelion the thermal wave penetrates the nucleus, sublimates a deep layer of CO2 up to aphelion, and remnants of these molecules are recondensed in the upper layers of the nucleus as it cools off. When the comet approaches the Sun post-aphelion, these remaining molecules are sublimated and produce the observed activity. It is beyond the scope of this paper to create a model to discriminate between these two hypothesis. What remains certain is that the double sublimation exhibited by 9P, 1P, 81P and 21P have profound implications for the interior models and structure of these cometary nuclei, and for our understanding of how a cometary nucleus sublimates into space.
The comet has an orbital period of 5.51 yr, thus apparitions repeat almost exactly every 11.02 years. Notice how the 1972, 1983, 1994, 2005 have perihelions in July 15th, 10th, 3rd, 5th, while in 1978, 1989, 2000 the perihelions were in January 11th, 4th, and 2nd. A complete SLC every 11 years would allow the determination of secular effects and the confirmation of postaphelion activity. In that regard, the comet reaches aphelion in 20080407 (YYYYMMDD) at elongation E = 42◦ and decreasing, thus approaching conjunction with the Sun. E = 90◦ and increasing in 20080926 when observation may commence, and reaches opposition in 20081218 at E = 176◦ . It again becomes increasingly difficult to observe in 20090309 at E = 90◦ and decreasing, but in 20091103 E = 90◦ and increasing. Finally, the comet reaches the turn on point, RON , in 20091124 at E = 108◦ and increasing. In conclusion the interval aphelion-RON will be only partially observable in 2008–2009. 5. Conclusions The main results of this work are: (a) 9P/Tempel 1 is a young object as measured by two definitions of age, P-AGE = 21 ± 2 cy and T-AGE = 11 ± 2 cy. This is in agreement with the smooth surface structure imaged by Deep Impact.
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(b) The comet exhibits double sublimation at turn on, showing a linear portion that changes to curvature at a break point RBP = −2.08 ± 0.05 AU pre-perihelion. This critical point has profound implications for our understanding of how a cometary nucleus sublimates into space. (c) Over 18 physical parameters of the comet have been updated and appear in Figs. 1 and 2. (d) A very precise mean absolute nuclear magnitude has been determined as VN (1, 1, 0) = 15.29 ± 0.04 (Table 1). (e) When this value is combined with a mean geometric albedo in the visual pV = 0.045 ± 0.009, an effective diameter DEFFE = 5.54 ± 0.5 km is derived from ground based observations in excellent agreement with the value derived from the Deep Impact Spacecraft (D = 5.47 ± 0.2 km). The information on this and other comets is regularly updated at the site: http://webdelprofesor.ula.ve/ciencias/ferrin. Acknowledgments To Oliver Hainaut and Carl Hergenrother for their suggestions to improve the scientific quality of this paper. To the Council for Scientific and Technological Development of the University of the Andes, for support through grant number C1281-04-05-B. References A’Hearn, M.F., and 32 colleagues, 2005. Deep Impact: Excavating Comet Tempel 1. Science 310, 258–264. Belton, M.J.S., Meech, K.J., 2003. Homing in on the period of 9P/Tempel. In: AAS DPS Meeting 35. Abstract 38.04. Belton, M.J.S., and 15 colleagues, 2005. Deep Impact: Working properties for the target nucleus—Comet 9P/Tempel 1. Space Sci. Rev. 117, 137–160. Biver, N., and 22 colleagues, 1997. Long-term evolution of the outgassing of Comet Hale–Bopp from radio observations. Earth Moon Planets 78, 5–11. Chen, J., Jewitt, D., 1994. On the rate at which comets split. Icarus 108, 265– 271. Delsemme, A.H., 1982. Chemical composition of the cometary nucleus. In: Wilkening, L. (Ed.), Comets. Univ. of Arizona Press, Tucson, AZ, pp. 85– 130. Fernandez, Y.R., Meech, K.J., Lisse, C.M., A’Hearn, M.F., Pittichová, J., Belton, M.J.S., 2003. The nucleus of Deep Impact target Comet 9P/Tempel 1. Icarus 164, 481–491. Ferrín, I., 2005. Secular light curve of Comet 28P/Neujmin 1, and of comets targets of Spacecraft, 1P/Halley, 9P/Tempel 1, 19P/Borrelly, 21P/Grigg–
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